Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability

Abstract

We study asynchronous replanning in a two population linear quadratic mean field game in which the populations may begin from different beliefs and hence use different plans. Each population observes its own aggregate trajectory and a public record of implemented revisions, while its continuation best response depends on the opponent's current plan. We identify the information required for replanning as the aggregate state at the end of the initial observation interval together with the opponent's active continuation plan. For linear observations, recoverability of this state-plan pair is characterized by a kernel inclusion, and a bounded factorization quantifies sensitivity to observation error. In particular, the required pair may be recoverable even when the full hidden belief is not. Once initialized, the public event record and the common best-response map recursively determine subsequent opponent plans, and the resulting local algorithm reproduces an ideal benchmark on every finite opportunity prefix; implemented revisions alternate as a consequence of best-response persistence. For finite populations, we derive an eventwise linear recursion for sampling errors, obtain finite prefix error bounds, and prove record matching for an autonomous deadband rule under a positive decision margin. Finally, we separate unique solvability of mutual continuation responses from stability of alternating responses, and show that at a pre-terminal Zeno accumulation, spectral stability together with a moving-boundary estimate yields convergence of the continuation plans to the equilibrium restarted from the actual limiting state.